Andrew,
I built a coil winder similar to what you are after – long, long ago.. – I used two stepper motors, one for the coil and one driving an M8 leadscrew carrying the yoke though which the wire is fed. Unlike screwcutting, this application never requires that you need to unhitch the carriage, or rewind to the thread start to restart. You always wind one direction, N turns, then the carriage reverses laying down the next layer of N turns at the same pitch, so much simpler, and quite different from an ELS – The typical ELS systems doing the rounds will in fact not work for this at all – will not allow the reverse pass layer to be wound..
My winder is so old – made it about 20 years ago Simple LCD with up/dn buttons to set number or turns per layer, number of turns total and wire thickness. I won't offer you my solution… – no Arduino back then and I used an Intel 8051 uP, and wrote the thing in assembler…
Are you arduino and/or software adept?
Joe